454 
Proceedings of Royal Society of Edinburgh. [sess. 
diameter of the specimen is thus obtained. A photograph of 
the apparatus is shown in fig. 3 mounted upon a tension specimen. 
The value of a unit of the scale was obtained by calibrating the 
instrument by a Whitworth measuring machine, and it was found 
that, with the scale 24 ’8 inches distant from the mirror, one 
division of the scale corresponded to one-millionth of an inch. 
At first some minor difficulties were experienced owing to the 
longer branches of the tubes being insufficiently rigid, and they 
were therefore trussed, with good effect, and afterwards pieces of 
hard wood, of square section, were forced down the tubes ; 
this overcame the difficulty completely. As the instrument was 
wholly of brass, some difficulty was experienced owing to small 
changes of temperature in the laboratory, which sometimes altered 
the zero of the instrument during a test ; this error was guarded 
against by lagging with chamois leather. 
The instrument, when used in conjunction with an apparatus 
for measuring longitudinal strain, gives a measure of Poisson’s 
ratio — if the material fulfils the conditions assumed by the theory 
m 
of elasticity ; and knowing the value of Young’s modulus E, we 
can easily calculate the modulus of shear C and the bulk modulus 
D from the formulae 
C = A -?L E 
2 m + 1 
D = 
E 
3 rn - 2 
As an example of this we may quote a test of a piece of 
machinery steel in tension, when the lateral extensometer above 
described and a Ewing extensometer were secured to the specimen. 
The experiment gave the following results 
Steel specimen 1*01 inches in diameter. 
Length under test 8 '00 inches. 
Ewing Extensometer, one division = 5 ^^ of an inch. 
Lateral Extensometer, one division = t,o oir.oo 0 an i nc ^* 
The accompanying table of observations (page 455) shows that 
the mean longitudinal strain per unit of length is ’0000825 inches, 
and the mean lateral strain ’0000206, corresponding to a value 
for m of 4 ’01, and the value of E, obtained in the usual manner, is 
30,250,000, the units being pounds and inches. 
